Variants of the block GMRES method for solving multi-shifted linear systems with multiple right-hand sides simultaneously

Sun, D., 2019, [Groningen]: University of Groningen. 152 p.

Research output: ThesisThesis fully internal (DIV)Academic

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  • Title and contents

    Final publisher's version, 192 KB, PDF document

  • Chapter 1

    Final publisher's version, 350 KB, PDF document

  • Chapter 2

    Final publisher's version, 1 MB, PDF document

  • Chapter 3

    Final publisher's version, 5 MB, PDF document

  • Chapter 4

    Final publisher's version, 757 KB, PDF document

  • Chapter 5

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  • Chapter 6

    Final publisher's version, 178 KB, PDF document

  • Bibliography

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  • Summary

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  • Samenvatting

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  • Acknowledgements

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  • Propositions

    Final publisher's version, 135 KB, PDF document

  • Complete thesis

    Final publisher's version, 7 MB, PDF document

  • Donglin Sun
This thesis concerns with the development of efficient Krylov subspace methods for solving sequences of large and sparse linear systems with multiple shifts and multiple right-hand sides given simultaneously. The need to solve this mathematical problem efficiently arises frequently in large-scale scientific and engineering applications. We introduce new robust variants of the shifted block Krylov subspace methods for this problem class. Shifted block Krylov subspace methods are computationally attractive to use as they can preserve the shift-invariance property of the block Krylov subspace and can use much larger search spaces for solving sequences of multi-shifted and multiple right-hand sides linear systems simultaneously.

In Chapter 1 we introduce the background about Krylov subspace methods and state the main research problems of this class of methods. In Chapter 2, we develop a new variant of the restarted shifted block Krylov method augmented with eigenvectors. In Chapter 3, we introduce a new flexible and deflated variant of the shifted block Krylov method solving the whole sequence of multi-shifted linear systems simultaneously based on an initial deflation strategy. In Chapter 4, we exploit the inexact breakdown strategy to develop a new shifted, augmented and deflated block Krylov method. In Chapter 5, we present spectrally preconditioned and initially deflated variants of block iterative Krylov solvers. Finally, in Chapter 6 we summarize the main characteristics of the algorithms proposed in the thesis, compare their numerical performance and draw some plans for future research.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Verstappen, Roel, Supervisor
  • Carpentieri, Bruno, Co-supervisor
  • Schaft, van der, Arjan, Assessment committee
  • Vuik, C., Assessment committee, External person
  • Bollhoefer, M., Assessment committee, External person
Award date15-Feb-2019
Place of Publication[Groningen]
Print ISBNs978-94-034-1357-0
Electronic ISBNs978-94-034-1356-3
Publication statusPublished - 2019

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